Conventional interpretation of two-dimensional and three-dimensional seismic data typically results in a converted data set representing the two-way seismic travel time of energy waves reflected by geological deposits formed beneath the Earth's surface. Data representing specific geological formations are called seismic horizons, and are oftentimes named after the formation or type of geological layer being represented.
In the past decade, horizon data has usually been created by a seismic interpreter using a computer or processor of some type and an industry-specific software package. At least some of the data is interpreted manually by digitization using a graphical display of the seismic data. However, much of the horizon data is computer-generated, using automated interpretation processes applied to parameters supplied by the interpreter.
As those of ordinary skill in the pertinent arts will appreciate, both lateral and vertical variations in the velocity of sound waves beneath the Earth's surface can result in the creation of an inaccurate structural interpretation of the subsurface when methods emphasizing only time-domain data are employed. Consequently, accurate predictions of prospective drilling locations and estimated geological formation depths are difficult to achieve.
One prior attempt to convert seismic horizon time data into depth data can be found in U.S. Pat. No. 5,648,937, issued Jul. 15, 1997 to Campbell, entitled Method and Apparatus for Correlating Geological Structure Horizons from Velocity Data to Well Observations, which describes a method of calibrating horizon depth data using the known depths of seismic horizons at well locations, and then creating an error map that conforms the horizon data to the well depths. The velocities used to convert the horizon time data to depth data prior to calibration are derived from the seismic data using known techniques employed during what is generally referred to as the seismic processing phase.
The method of Campbell has proven to be deficient, however, in that it is fundamentally only a calibration technique wherein an approximate horizon depth value is adjusted so as to be consistent with known depths of existing wells, rather than a method of deriving a geophysically-consistent velocity function model between well locations using interval velocities from both well data and interpreted seismic horizons. As discussed in the background section of the Campbell patent, for example, it is well known that the use of processing velocities for depth conversion is highly susceptible to cumulative calculation error.
Another deficiency of the Campbell method is that processing velocities are not in fact the true seismic velocities of the Earth, but estimates based on their effectiveness as parameters in the processing of data, the goal being to derive the best possible data images or signal-to-noise characteristics of a seismic reflector set (see, for example, prior art FIG. 1). Therefore, even after calibration at well locations, there is a great chance of significant computational error and uncertainty as to the actual geological conditions present between wells. In addition, irregular lateral deviations of processing velocities, which are common, can result in large computational errors in associated depth values.
In situations where existing well data is located far away, or where data is derived from wells located on the other side of a fault or are for some other reason unsuitable as a basis for data extrapolation, the method of Campbell is simply inadequate for establishing the relatively precise drilling depth estimates sought by modern geophysicists and drilling investors.
Another prior attempt to improve interpreted seismic results can be found in an article entitled Depth Conversion of Tangguh Gas Fields, published in the October 2002 edition of the exploration publication THE LEADING EDGE, in which authors Keho and Samsu attempt to show that by applying linear regression to a plurality of average velocities of the uppermost (shallowest) layer, the Vo and K values present in the equation Vavg=Vo+KZ (where Vavg is the average velocity, Vo is the velocity at zero depth, K is the compaction factor, and Z is the depth) can be derived so as to better estimate the horizon depth values associated therewith (see, for example, prior art FIG. 2). This and many other prior art techniques result from variations of the equation Vi=V0+KZ, which abounds in the literature and defines the instantaneous velocity as a linear function of depth.
In the mentioned paper, Keho and Samsu show that the Vo and K values for the shallowest layer can be extracted by applying linear regression to a plot of the average velocities versus formation top depths at the wells, so long as Vo and K are approximately constant in the area containing the wells. As seen in prior art FIGS. 3 and 4, for example, a conventional plot of seismic velocity versus horizon depth can be established between and amongst known well locations, in which velocity values are extracted by comparison of the formation top depth intervals and the horizon seismic time intervals. In this model, the projected velocity at zero depth is defined as Vo and the compaction factor K is indicated by the slope of the line (see FIG. 3). Even though the function is approximately linear, however, the data points do not lie exactly on the extracted line and therefore exact well ties will not result without additional calibration. In this case, well ties were achieved by holding K constant and mapping V0 over the entire geographic area. More importantly, in instances where the interval velocity is not a linear function with respect to depth, which is the case for the second layer in their article, Keho and Samsu conclude this method is inadequate for estimating accurate drilling depth values.
In an article entitled Analytic Velocity Functions (THE LEADING EDGE, July 1995, pp. 775-782), Marsden et al. mention a method of obtaining a better linear fit for interval velocities as a function of depth called “robust fitting” (from Beltrao et al., GEOPHYSICS, 1991), where data points are weighted less as they deviate from the general trend. This weighting, however, is not based on geological assumptions and the resulting depth maps must still be calibrated at well locations using techniques such as error mapping (Japsen, AAPG Bulletin 1993). In their conclusion, Marsden et al. recommend in the conclusion the use of velocity logs to compute analytic functions and map the parameter variations (V0 and K were two of the three parameters). This method, however, also has pitfalls as velocity logs are not always readily available, and it also requires considerable effort by the interpreter to derive the functions, map the parameters, and hopefully estimate the reliability of the values. Moreover, those of skill in the art will appreciate that a linear model establishing velocity increase as a function of depth can only result if the increase is due to compaction factors alone. Such an assumption, however, is often incorrect. For example, lithological changes that have occurred slowly over a great deal of geologic time, lateral and/or vertical changes in the composition of the sedimentary layer, and an inadequate number of horizons used to define layers with different velocity functions can all invalidate the linear model assumption.
Those of skill in the art will also appreciate that gridding of the data values is required, said gridding generally being carried out by means of computer mapping programs and previously known depth conversion techniques. In practice, most gridding processes compute original input data at evenly spaced bin intervals, so that computations can be carried out in a simple and efficient manner. Then, using the same bin intervals, gridded time values for deeper horizons are calculated directly beneath those of the shallower horizons, thereby making subsequent interval computations for time, thickness and velocity relatively fast and easy for the interpreter. In addition, there are often fewer data points after the gridding process, which also improves the data processing speed.
Gridding has many inherent shortcomings, however. For example, since gridding is fundamentally a sampling process, the accuracy of representing the input data set is primarily a combined function of the sampling interval and the variability or horizontal frequency of the input data. Moreover, in the case of geological mapping, exact well ties and determinations regarding the precise location and extent of faults are particularly problematic when gridded data is used.
For example, wells are rarely located exactly in the center of a grid bin, so the gridded depth values generally do not tie the original well values. In addition, faults can cause abrupt changes to geological formation structure, and bin intervals must be small enough to adequately sample such changes. As a result, precise computations around fault planes are necessarily compromised, especially when several finely spaced horizon time picks are averaged into one value for a grid bin disposed next to a fault plane. When applied to depth conversions, estimates using only gridding processes to determine the location of geological formations will incorporate error factors that are simply unacceptable to modern geophysicists and drilling investors.
In certain applications, three-dimensional sampling is also employed, which can create such a massive data volume that an extremely large amount of random-access memory is required, even though the problems associated with faulting and non-exact well ties are not significantly reduced. For example, when three-dimensional sampling is employed, not only are the geographic locations inaccurate, the depths of the formation tops are also. In short, even if a geophysically consistent solution of the velocity model between well locations could be determined, conventional gridding processes simply do not provide adequate precision as to allow an accurate conversion of horizon time data into depth values.
In view of the many longstanding problems present in the prior art, there is clearly a significant need for more reliable methods of converting interpreted seismic horizons derived from time values into accurately estimated depth values. The present invention is therefore directed to the development of more reliable methods of solving these problems.